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Simplifying 26x2 + -3x + -22 = 0 Reorder the terms: -22 + -3x + 26x2 = 0 Solving -22 + -3x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.8461538462 + -0.1153846154x + x2 = 0 Move the constant term to the right: Add '0.8461538462' to each side of the equation. -0.8461538462 + -0.1153846154x + 0.8461538462 + x2 = 0 + 0.8461538462 Reorder the terms: -0.8461538462 + 0.8461538462 + -0.1153846154x + x2 = 0 + 0.8461538462 Combine like terms: -0.8461538462 + 0.8461538462 = 0.0000000000 0.0000000000 + -0.1153846154x + x2 = 0 + 0.8461538462 -0.1153846154x + x2 = 0 + 0.8461538462 Combine like terms: 0 + 0.8461538462 = 0.8461538462 -0.1153846154x + x2 = 0.8461538462 The x term is -0.1153846154x. Take half its coefficient (-0.0576923077). Square it (0.003328402368) and add it to both sides. Add '0.003328402368' to each side of the equation. -0.1153846154x + 0.003328402368 + x2 = 0.8461538462 + 0.003328402368 Reorder the terms: 0.003328402368 + -0.1153846154x + x2 = 0.8461538462 + 0.003328402368 Combine like terms: 0.8461538462 + 0.003328402368 = 0.849482248568 0.003328402368 + -0.1153846154x + x2 = 0.849482248568 Factor a perfect square on the left side: (x + -0.0576923077)(x + -0.0576923077) = 0.849482248568 Calculate the square root of the right side: 0.921673613 Break this problem into two subproblems by setting (x + -0.0576923077) equal to 0.921673613 and -0.921673613.Subproblem 1
x + -0.0576923077 = 0.921673613 Simplifying x + -0.0576923077 = 0.921673613 Reorder the terms: -0.0576923077 + x = 0.921673613 Solving -0.0576923077 + x = 0.921673613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0576923077' to each side of the equation. -0.0576923077 + 0.0576923077 + x = 0.921673613 + 0.0576923077 Combine like terms: -0.0576923077 + 0.0576923077 = 0.0000000000 0.0000000000 + x = 0.921673613 + 0.0576923077 x = 0.921673613 + 0.0576923077 Combine like terms: 0.921673613 + 0.0576923077 = 0.9793659207 x = 0.9793659207 Simplifying x = 0.9793659207Subproblem 2
x + -0.0576923077 = -0.921673613 Simplifying x + -0.0576923077 = -0.921673613 Reorder the terms: -0.0576923077 + x = -0.921673613 Solving -0.0576923077 + x = -0.921673613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0576923077' to each side of the equation. -0.0576923077 + 0.0576923077 + x = -0.921673613 + 0.0576923077 Combine like terms: -0.0576923077 + 0.0576923077 = 0.0000000000 0.0000000000 + x = -0.921673613 + 0.0576923077 x = -0.921673613 + 0.0576923077 Combine like terms: -0.921673613 + 0.0576923077 = -0.8639813053 x = -0.8639813053 Simplifying x = -0.8639813053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9793659207, -0.8639813053}
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